MTH 263 Exam #1
Questions and Exercises to Guide Your Review
Questions:
1. What is the average rate of change of the function 𝑔(𝑡) over the interval from 𝑡 = 𝑎 to
𝑡 = 𝑏? How is it related to a secant line?
2. What limit must be calculated to find the rate of change of a function 𝑔(𝑡) at 𝑡 = 𝑡0 ?
3. Does the existence and value of the limit of a function 𝑓(𝑥) as 𝑥 approaches 𝑐 ever
depend on what happens at 𝑥 = 𝑐?
4. What function behaviors might occur for which the limit may fail to exist?
5. What conditions must be satisfied by a function if it is to be continuous at an interior
point of its domain? At an endpoint?
6. What are the basic types of discontinuity?
7. What does it mean for a function to have the Intermediate Value Property? What
conditions guarantee that a function has this property over an interval?
8. What are horizontal and vertical asymptotes?
9. What is the derivative of a function?
10. What role does the derivative play in defining slope, tangents and rates of change?
11. Describe geometrically when a function typically does not have a derivative at a point?
Exercises:
Chapter 2 Review: 5, 7, 13, 15, 25, 33, 35, 37, and 43